Semiclassical low energy scattering for one-dimensional Schr\"odinger operators with exponentially decaying potentials

We consider semiclassical Schr\"odinger operators on the real line of the form $$H(\hbar)=-\hbar^2 \frac{d^2}{dx^2}+V(\cdot;\hbar)$$ with $\hbar>0$ small. The potential $V$ is assumed to be smooth, positive and exponentially decaying towards infinity. We establish semiclassical global representations of Jost solutions $f_\pm(\cdot,E;\hbar)$ with error terms that are uniformly controlled for small $E$ and $\hbar$, and construct the scattering matrix as well as the semiclassical spectral measure associated to $H(\hbar)$. This is crucial in order to obtain decay bounds for the corresponding wave and Schr\"odinger flows. As an application we consider the wave equation on a Schwarzschild background for large angular momenta $\ell$ where the role of the small parameter $\hbar$ is played by $\ell^{-1}$. It follows from the results in this paper and \cite{DSS2}, that the decay bounds obtained in \cite{DSS1}, \cite{DS} for individual angular momenta $\ell$ can be summed to yield the sharp $t^{-3}$ decay for data without symmetry assumptions.Comment: 44 pages, minor modifications in order to match the published version, will appear in Annales Henri Poincar

A systematic characterization of cognitive techniques for learning from textual and pictorial representations

Pictorial representations can play a pivotal role in both printed and digital learning material. Although there has been extensive research on cognitive techniques and strategies for learning from text, the same cannot be said for static and dynamic pictorial representations. In this paper we propose a systematic characterization of cognitive learning techniques that is founded on both theoretical and empirical research. The characterization relates the learning techniques to classes of cognitive processes as well as to textual and pictorial representations. We show how successful strategies for learning from both plain text and illustrated text are covered by the characterization. We also exemplify how the construction of new strategies for pictorial representations can be informed by the characterization

Electronic spectra of polyatomic molecules with resolved individual rotational transitions

The density of rotational transitions for a polyatomic molecule is so large that in general many such transitions are hidden under the Doppler profile, this being a fundamental limit of conventional high resolution electronic spectroscopy. We present here the first Doppler-free cw two-photon spectrum of a polyatomic molecule. In the case of benzene, 400 lines are observed of which 300 are due to single rotational transitions, their spacing being weil below the Doppler profile. The resolution so achieved is 1.5 X 10'. Benzene is a prototype planar molecule taken to have D •• symmetry in the ground as weil as in the first excited state. From our ultra-high resolution results it is found that benzene in the excited SI state i8 a symmetrical rotor to a high degree. A negative inertial defect is found for the excited state. The origin of this inertial defect is discused

Evaluation of higher-order time-domain perturbation theory of photon diffusion on breast-equivalent phantoms and optical mammograms

Time-domain perturbation theory of photon diffusion up to third order was evaluated for its accuracy in deducing optical properties of breast tumors using simulated and physical phantoms and by analyzing 141 projection mammograms of 87 patients with histology-validated tumors that had been recorded by scanning time-domain optical mammography. The slightly compressed breast was modeled as (partially) homogeneous diffusely scattering infinite slab containing a scattering and absorbing spherical heterogeneity representing the tumor. Photon flux densities were calculated from densities of transmitted photons, assuming extended boundary conditions. Explicit formulas are provided for second-order changes in transmitted photon density due to the presence of absorbers or scatterers. The results on phantoms obtained by perturbation theory carried up to third order were compared with measured temporal point spread functions, with numerical finite-element method (FEM) simulations of transmitted photon flux density, with results obtained from the diffraction of diffuse photon density waves, and from Pade approximants. The breakdown of first-, second-, and third-order perturbation theory is discussed for absorbers and a general expression was derived for the convergence of the Born series in this case. Taking tumor optical properties derived by the diffraction model as reference we conclude that estimates of tumor absorption coefficients by perturbation theory agree with reference values within +/-25% in only 65% (first order), 66% (second order), and 77% (third order) of all mammograms analyzed. In the remaining cases tumor absorption is generally underestimated due to the breakdown of perturbation theory. On average the empirical Pade approximants yield tumor absorption coefficients similar to third-order perturbation theory, yet at noticeable lower computational efforts

Ketamine treatment for depression: opportunities for clinical innovation and ethical foresight

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this record.We present a review and analysis of the ethical considerations in off-label ketamine use for severe, treatment-resistant depression. The analysis of ethical considerations is contextualised in an overview of the evidence for ketamine use in depression, and a review of the drug's safety profile. We find that, based on current evidence, ketamine use for severe, treatment-resistant depression does not violate ethical principles; however, clinicians and professional bodies must take steps to ensure that guidelines for good practice are enacted, that all experimental and trial data are made available through national registries, and that the risk potential of ketamine treatment continues to be monitored and modelled. We conclude with a set of key recommendations for oversight bodies that would support safe, effective, and ethical use of ketamine in depression

Uptake, biodistribution, and time course of naked plasmid DNA trafficking after intratumoral in vivo jet injection

Nonviral jet injection is an applicable technology for in vivo gene transfer of naked DNA. However, little is known about the biodistribution and clearance of jet-injected DNA, or about its localization within tissue and cells. Therefore, in this study we analyzed the intratumoral and systemic biodistribution of jet-injected naked DNA in human colon carcinoma-bearing NCr-nu/nu mice, which were jet-injected with the pCMVbeta plasmid DNA. Intratumoral and systemic plasmid DNA biodistribution was analyzed 5, 10, 20, and 40 min and 3, 6, 24, 48, and 72 hr after jet injection, using quantitative real-time polymerase chain reaction. In the tumors, a rapid drop in naked DNA load within 24 hr of jet injection was shown. Detailed analysis of intratumoral distribution of rhodamine-labeled DNA revealed the presence of plasmid DNA within tumor cells 5 min after jet injection and further accumulation of significant DNA amounts in the cell nuclei 30 to 60 min after jet injection. In the blood, DNA amounts rapidly dropped within 10 to 40 min of jet injection to less than 0.001 pg of plasmid per 250 ng of tissue DNA and only minimal plasmid DNA dissemination was detected in liver, lung, spleen, kidney, and ovaries, which was cleared 3 to 6 hr after jet injection. By contrast, in heart, bone marrow, and brain almost no plasmid DNA was detectable

Effectiveness of ammonia reduction on control of fine particle nitrate

In some regions, reducing aerosol ammonium nitrate (NH4NO3) concentrations may substantially improve air quality. This can be accomplished by reductions in precursor emissions, such as nitrogen oxides (NOx) to lower nitric acid (HNO3) that partitions to the aerosol, or reductions in ammonia (NH3) to lower particle pH and keep HNO3 in the gas phase. Using the ISORROPIA-II thermodynamic aerosol model and detailed observational data sets, we explore the sensitivity of aerosol NH4NO3 to gas-phase NH3 and NOx controls for a number of contrasting locations, including Europe, the United States, and China. NOx control is always effective, whereas the aerosol response to NH3 control is highly nonlinear and only becomes effective at a thermodynamic sweet spot. The analysis provides a conceptual framework and fundamental evaluation on the relative value of NOx versus NH3 control and demonstrates the relevance of pH as an air quality parameter. We find that, regardless of the locations examined, it is only when ambient particle pH drops below an approximate critical value of 3 (slightly higher in warm and slightly lower in cold seasons) that NH3 reduction leads to an effective response in PM2.5 mass. The required amount of NH3 reduction to reach the critical pH and efficiently decrease NH4NO3 at different sites is assessed. Owing to the linkage between NH3 emissions and agricultural productivity, the substantial NH3 reduction required in some locations may not be feasible. Finally, controlling NH3 emissions to increase aerosol acidity and evaporate NH4NO3 will have other effects, beyond reduction of PM2.5 NH4NO3, such as increasing aerosol toxicity and potentially altering the deposition patterns of nitrogen and trace nutrients.</p

Changes in trabecular bone, hematopoiesis and bone marrow vessels in aplastic anemia, primary osteoporosis, and old age

Retrospective histologic analyses of bone biopsies and of post mortem samples from normal persons of different age groups, and of bone biopsies of age- and sex-matched groups of patients with primary osteoporosis and aplastic anemia show characteristic age dependent as well as pathologic changes including atrophy of osseous trabeculae and of hematopoiesis, and changes in the sinusoidal and arterial capillary compartments. These results indicate the possible role of a microvascular defect in the pathogenesis of osteoporosis and aplastic anemia

Imitation in Large Games

In games with a large number of players where players may have overlapping objectives, the analysis of stable outcomes typically depends on player types. A special case is when a large part of the player population consists of imitation types: that of players who imitate choice of other (optimizing) types. Game theorists typically study the evolution of such games in dynamical systems with imitation rules. In the setting of games of infinite duration on finite graphs with preference orderings on outcomes for player types, we explore the possibility of imitation as a viable strategy. In our setup, the optimising players play bounded memory strategies and the imitators play according to specifications given by automata. We present algorithmic results on the eventual survival of types

A network model to investigate structural and electrical properties of proteins

One of the main trend in to date research and development is the miniaturization of electronic devices. In this perspective, integrated nanodevices based on proteins or biomolecules are attracting a major interest. In fact, it has been shown that proteins like bacteriorhodopsin and azurin, manifest electrical properties which are promising for the development of active components in the field of molecular electronics. Here we focus on two relevant kinds of proteins: The bovine rhodopsin, prototype of GPCR protein, and the enzyme acetylcholinesterase (AChE), whose inhibition is one of the most qualified treatments of Alzheimer disease. Both these proteins exert their functioning starting with a conformational change of their native structure. Our guess is that such a change should be accompanied with a detectable variation of their electrical properties. To investigate this conjecture, we present an impedance network model of proteins, able to estimate the different electrical response associated with the different configurations. The model resolution of the electrical response is found able to monitor the structure and the conformational change of the given protein. In this respect, rhodopsin exhibits a better differential response than AChE. This result gives room to different interpretations of the degree of conformational change and in particular supports a recent hypothesis on the existence of a mixed state already in the native configuration of the protein.Comment: 25 pages, 12 figure